Optimal. Leaf size=39 \[ \frac{x^{m+1} \, _2F_1\left (1,\frac{m+1}{7};\frac{m+8}{7};-\frac{b x^7}{a}\right )}{a (m+1)} \]
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Rubi [A] time = 0.0085292, antiderivative size = 39, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {364} \[ \frac{x^{m+1} \, _2F_1\left (1,\frac{m+1}{7};\frac{m+8}{7};-\frac{b x^7}{a}\right )}{a (m+1)} \]
Antiderivative was successfully verified.
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Rule 364
Rubi steps
\begin{align*} \int \frac{x^m}{a+b x^7} \, dx &=\frac{x^{1+m} \, _2F_1\left (1,\frac{1+m}{7};\frac{8+m}{7};-\frac{b x^7}{a}\right )}{a (1+m)}\\ \end{align*}
Mathematica [A] time = 0.0071701, size = 41, normalized size = 1.05 \[ \frac{x^{m+1} \, _2F_1\left (1,\frac{m+1}{7};\frac{m+1}{7}+1;-\frac{b x^7}{a}\right )}{a (m+1)} \]
Antiderivative was successfully verified.
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Maple [F] time = 0.036, size = 0, normalized size = 0. \begin{align*} \int{\frac{{x}^{m}}{b{x}^{7}+a}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x^{m}}{b x^{7} + a}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{x^{m}}{b x^{7} + a}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x^{m}}{b x^{7} + a}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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